1. Simplify the following expression by removing the innermost brackets first:
[tex]\[
\begin{array}{l}
118 - (16 - (5 - \overline{4 - 1})) \\
= 118 - (16 - (5 - 3)) \\
= 118 - (16 - 2) \\
= 118 - 14 \\
= 104
\end{array}
\][/tex]

Example 3: Simplify the expression using the order of operations (ODMAS):

[tex]\[
90 + \{10 + 15 \text{ of } 3 - (20 + 30 - 45 + 5)\}
\][/tex]
[tex]\[
= 90 + \{10 + 15 \text{ of } 3 - (20 + 30 - 9)\}
\][/tex]
[tex]\[
= 90 + \{10 + 15 \text{ of } 3 - 41\}
\][/tex]
[tex]\[
= 90 + 14
\][/tex]
[tex]\[
= 104
\][/tex]

Exercise 1.2

1. Simplify:

(i) [tex]$(-76) + 24 + 80 + (-28) = $[/tex]
(ii) [tex]$(-21) + (-9) + (-30) + (-5) = $[/tex]
(iii) [tex]$-20 + 12 \times 3 = $[/tex]
(iv) [tex]$158 \times (-46) + (-158) \times 54 = $[/tex]
(v) [tex]$(-198 \times -46) + (2 \times 46) = $[/tex]
(vi) [tex]$-7(-50 + 35 + 15 - 4) = $[/tex]

2. Simplify the following:

(i) [tex]$18 + (12 \div -2) = $[/tex]
(ii) [tex]$17 - [3 + 2 - \{-4 + (2 - 3)\}] = $[/tex]
(iii) [tex]$17 - [3 + 2 - \{-4 + (12 - 3)\}] = $[/tex]
(iv) [tex]$126 \div [-8 - 6 + \{3 - (-12 + 8)\}] = $[/tex]
(v) [tex]$5 - [5 - \{5 - (5 - 5)\}] = $[/tex]
(vi) [tex]$14 - 2[8 + 3\{2 - 4 + (3 - 2)\}] = $[/tex]
(vii) [tex]$10 - \frac{1}{3} \text{ of } [9 \div (-3) + \{16 - 2 \times 3 - 4(4 - 6)\}] = $[/tex]

3. Simplify:

(i) [tex]$\{2 + 2 \times 2 + (-2)\} \div 2 = $[/tex]
(ii) [tex]$1 - 2 + 2 \times (-2) + (-2) - 1 - 21 = $[/tex]
(iii) [tex]$\{18 \div (-6)\} \div (-24) \div \{(-24) \div (-8)\} = $[/tex]
(iv) [tex]$(-15) \{(-15) \div 3 - (-1)\} \div (-15) = $[/tex]
(v) [tex]$(-1) - [-1 - \{-1 - (-1)\}] = $[/tex]

4. Name the grouping symbols used in the following expression:
[tex]\[
15 \div [3 - \{18 - (19 - \overline{5 - 3})\}]
\][/tex]

5. Simplify:

(i) [tex]$27 - [5 + \{28 - (29 - 7)\}] = $[/tex]
(ii) [tex]$48 - [18 - \{16 - 5 - \overline{4 - 1}\}] = $[/tex]
(iii) [tex]$39 - [23 - \{29 - (17 - \overline{9 - 3})\}] = $[/tex]
(iv) [tex]$15 - (-3) \{4 - \overline{-3}\} \div 3[\{5 + (-3) \times (-6)\}] = $[/tex]

To simplify the given expression, we will follow the BODMAS/PEMDAS rules, which stand for:

- Brackets/Parentheses
- Orders (i.e., powers and square roots, etc.)
- Division and Multiplication (from left to right)
- Addition and Subtraction (from left to right)

The given equation is:

[tex]\[ 90 + \{10 + 15 \times 3 - (20 + 30 - 45 + 5)\} \][/tex]

Let's solve this step-by-step.

### Step 1: Solve the innermost bracket
First, we handle the innermost expressions within the brackets:

[tex]\[ (20 + 30 - 45 + 5) \][/tex]

This can be calculated as:

[tex]\[ 20 + 30 = 50 \][/tex]
[tex]\[ 50 - 45 = 5 \][/tex]
[tex]\[ 5 + 5 = 10 \][/tex]

Therefore,

[tex]\[ (20 + 30 - 45 + 5) = 10 \][/tex]

### Step 2: Substitute the result back into the expression

Now substitute the evaluated expression back:

[tex]\[ 90 + \{10 + 15 \times 3 - 10\} \][/tex]

### Step 3: Perform the multiplication

Next, solve the multiplication:

[tex]\[ 15 \times 3 = 45 \][/tex]

Substitute this back into the expression:

[tex]\[ 90 + \{10 + 45 - 10\} \][/tex]

### Step 4: Handle the addition and subtraction inside the curly brackets

Now add and subtract within the brackets:

[tex]\[ 10 + 45 = 55 \][/tex]
[tex]\[ 55 - 10 = 45 \][/tex]

So we have:

[tex]\[ 90 + 45 \][/tex]

### Step 5: Perform the final addition

Finally, add the remaining numbers:

[tex]\[ 90 + 45 = 135 \][/tex]

### Conclusion

The simplified result of the expression is:

[tex]\[ \boxed{135} \][/tex]